A050490 a(n) = C(n)*(11n+1) where C(n) = Catalan numbers (A000108).

1, 12, 46, 170, 630, 2352, 8844, 33462, 127270, 486200, 1864356, 7171892, 27665596, 106977600, 414538200, 1609344270, 6258307590, 24373220520, 95050101300, 371125269900, 1450670612820, 5676173948640, 22230262964520, 87137141867100, 341824599040860, 1341897206800752

Offset: 0

Author

Barry E. Williams, Dec 27 1999

Keywords

• easy
• nonn

References

• Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Column k=11 of A330965.

Cf. A017281, A027810, A000108.

Programs

Magma

[Catalan(n)*(11*n+1):n in [0..25] ]; // Marius A. Burtea, Jan 05 2020

Mathematica

Table[CatalanNumber[n](11n+1),{n,0,20}] (* Harvey P. Dale, Jul 12 2018 *)

Formula

From R. J. Mathar, Feb 13 2015: (Start)

5*(n+1)*a(n) + (-29*n-1)*a(n-1) + 18*(2*n-3)*a(n-2) = 0.

-(n+1)*(11*n-10)*a(n) + 2*(11*n+1)*(2*n-1)*a(n-1) = 0. (End)

G.f.: (5 - 9*x - 5*sqrt(1 - 4*x))/(x*sqrt(1 - 4*x)). - Amiram Eldar, Jul 08 2023

Extensions

Terms a(21) and beyond from Andrew Howroyd, Jan 05 2020